Question

tan theta . tan 2 theta= 1 then, find the value of cos 2 theta?​

Answer 1

ANSWER

$\tan2 \alpha = 1 \\ \\ take \: square \: of \: both \: side..... \\ \\ { \tan}^{2} 2 \alpha = 1 \\ \\ { \sec}^{2} 2 \alpha - 1 = 1 \\ \\ { \sec }^{2} 2 \alpha = 2 \\ \\ \sec2 \alpha = \sqrt{2} \\ \\ \cos2 \alpha = \frac{1}{ \sqrt{2} } \\ |answer|$

IDENTITY USED.....

${ \tan}^{2} \alpha + 1 = { \sec }^{2} \alpha \\ \\ \sec \alpha = \frac{1}{ \cos \alpha }$

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Answer 2

Answer is given below

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